A Generalization of Source of Semiprimeness

Basit Öğe Kaydı
dc.contributor.authorCamcı, Didem Karalarlıoğlu
dc.contributor.authorYeşil, Didem
dc.contributor.authorMekera, Rasie
dc.contributor.authorCamcı, Çetin
dc.date.accessioned2025-05-29T05:37:07Z
dc.date.available2025-05-29T05:37:07Z
dc.date.issued2024
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractThis paper characterizes the semigroup ideal $\mathcal{L}_{R}^{n}(I)$ of a ring $R$, where $I$ is an ideal of $R$, defined by $\mathcal{L}_{R}^{0}(I)=I$ and $\mathcal{L}_{R}^{n}(I)=\{a\in R \mid aRa\subseteq \mathcal{L}_{R}^{n-1}(I)\}$, for all $n\in \mathbb{Z}^+$, the set of all the positive integers. Moreover, it studies the basic properties of the set $\mathcal{L}_{R}^{n}(I)$ and defines $n$-prime ideals, $n$-semiprime ideals, $n$-prime rings, and $n$-semiprime rings. This study also investigates relationships between the sets $\mathcal{L}_{R}(I)$ and $\mathcal{L}_{R}^{n}(I)$ and exemplifies some of the related properties. It obtains the main results concerning prime rings and prime ideals by the properties of the set $\mathcal{L}_{R}^{n}(I)$.
dc.identifier.doi10.53570/jnt.1581076
dc.identifier.endpage68
dc.identifier.issn2149-1402
dc.identifier.issue49
dc.identifier.startpage62
dc.identifier.urihttps://doi.org/10.53570/jnt.1581076
dc.identifier.urihttps://hdl.handle.net/20.500.12428/31613
dc.language.isoen
dc.publisherNaim ÇAĞMAN
dc.relation.ispartofJournal of New Theory
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_DergiPark_20250529
dc.subjectSource of semiprimeness
dc.subjectsemiprime rings
dc.subjectsemiprime ideals
dc.subjectprime rings
dc.subjectprime ideals
dc.titleA Generalization of Source of Semiprimeness
dc.typeResearch Article

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